City E and City F were 429 km apart. A van travelled from City E towards City F. At the same time, a lorry started from City F to City E. After travelling 1
34 h, the two vehicles were still 156 km apart. If the ratio of the average speed of the lorry to that of the van was 6 : 7, find
- the average speed of the van.
- the time taken for them to meet travelling the rest of the journey. Express your answer in h.
(a)
Distance covered in 1
34 h by the two vehicles
= 429 - 156
= 273 km
Combined speed of the two vehicles
= 273 ÷
74 = 273 x
47 = 156 km/h
Average speed of the lorry : Average speed of the van = 6 : 7
6 u + 7 u = 13 u
13 u = 156
1 u = 156 ÷ 13 = 12
Average speed of the van
= 7 u
= 7 x 12
= 84 km/h
(b)
Time taken for the lorry and the van to meet travelling the rest of the journey
= 156 ÷ 156
= 1 h
Answer(s): (a) 84 km/h; (b) 1 h